In [1]} and [2]}, it was shown that \([-1]\) -shifted derived schemes (resp. stacks) can be written locally as the critical locus of a functional on a smooth scheme, i.e. can be covered by critical charts of the form \((R,U,f,i)\) , where \(R\subset X\)  is open, \(U\)  is a smooth scheme, \(f:U\rightarrow \mathbb {C}\)  a regular map, and \(i:R\rightarrow U\)  a closed embedding such that \(i(R)={\rm Crit}(f)\) , and there is a way to compare intersecting critical charts. More formally, such a scheme (resp. stack) carries a d-critical structure \(s\) , a notion that we will introduce below. In [3]}, Joyce and collaborators has constructed the Donaldson-Thomas perverse sheaf \(P_{X,s}\)  carrying a monodromic mixed Hodge module for a d-critical scheme or stack \((X,s)\) , with extra data called orientation \(K_X^{1/2}\) . Its restriction to a critical \((R,U,f,i)\)  is given by:
\(P_{X,s}|_R:=\mathcal {PV}_{U,f}\otimes _{\mathbb {Z}/2\mathbb {Z}}Q_{R,U,f,i}\) 
